Model Adaptation for Non Linear Elliptic Equations in Mixed Form Existence of Solutions and Numerical Strategies - Archive ouverte HAL Access content directly
Journal Articles ESAIM: Mathematical Modelling and Numerical Analysis Year : 2022

Model Adaptation for Non Linear Elliptic Equations in Mixed Form Existence of Solutions and Numerical Strategies

(1) , (2)
1
2

Abstract

Depending on the physical and geometrical properties of a given porous medium, fluid flow can behave differently, going from a slow Darcian regime to more complicated Brinkman or even Forchheimer regimes for high velocity. The main problem is to determine where in the medium one regime is more adequate than others. In order to determine the low-speed and high-speed regions, this work proposes an adaptive strategy which is based on selecting the appropriate constitutive law linking velocity and pressure according to a threshold criterion on the magnitude of the fluid velocity itself. Both theoretical and numerical aspects are considered and investigated, showing the potentiality of the proposed approach. From the analytical viewpoint, we show existence of weak solutions to such model under reasonable hypotheses on the constitutive laws. To this end, we use a variational approach identifying solutions with minimizers of an underlying energy functional. From the numerical viewpoint, we propose a one-dimensional algorithm which tracks the transition zone between the low- and high-speed regions. By running numerical experiments using this algorithm, we illustrate some interesting behaviors of our adaptive model on academic cases and on small networks of intersecting fractures.
Fichier principal
Vignette du fichier
Model Adaptation for Non-Linear Elliptic Equations in Mixed Form Existence of Solutions and Numerical Strategies.pdf (1.85 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03625900 , version 1 (31-03-2022)

Licence

Attribution - CC BY 4.0

Identifiers

Cite

Alessio Fumagalli, Francesco Saverio Patacchini. Model Adaptation for Non Linear Elliptic Equations in Mixed Form Existence of Solutions and Numerical Strategies. ESAIM: Mathematical Modelling and Numerical Analysis, 2022, 56 (2), pp.565 - 592. ⟨10.1051/m2an/2022016⟩. ⟨hal-03625900⟩

Collections

IFP INSMI
35 View
19 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More